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Author:   David R. Finkelstein
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1996
Dimensions:   Width: 15.50cm , Height: 3.00cm , Length: 23.50cm
Weight:   0.902kg
ISBN:  

9783642646126

ISBN 10:   3642646123
Pages:   578
Publication Date:   14 March 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Act 1 One.- 1. Quantum Action.- 1.1 The Quantum Evolution.- 1.2 Quantum Concepts.- 1.2.1 Initial and Final Modes.- 1.2.2 Quantum Relativity.- 1.2.3 Time.- 1.2.4 Being, Becoming and Doing.- 1.2.5 Ontism and Praxism.- 1.3 Quantum Entities.- 1.3.1 Sharp Actions.- 1.3.2 Complete Actions.- 1.3.3 Quantum Acts.- 1.3.4 Quantum Activity.- 1.3.5 Quantum Superposition.- 1.4 The Quantum Project.- 1.4.1 Understanding Quantum Theory.- 1.4.2 The Quantum-Relativity Analogy.- 1.5 Quantum Nomenclature.- 1.6 Summary.- 2. Elementary Quantum Experiments.- 2.1 Malusian Experiments.- 2.2 Adjoint.- 2.3 Action Vector Semantics.- 2.3.1 General Actions.- 2.3.2 Action Vectors of Classical Systems.- 2.3.3 Equivalent Actions.- 2.3.4 Semantics and Ensembles.- 2.3.5 Logic, Kinematics, and Dynamics.- 2.3.6 Complex Vectors.- 2.3.7 Adjoint and Time Reversals.- 2.4 Quantum and Classical Kinematics.- 2.4.1 Classical Kinematics.- 2.4.2 Bohr Quantum Principle.- 2.4.3 Quantum Kinematics.- 2.4.4 Logical Modes.- 2.4.5 Causes.- 2.4.6 Completeness.- 2.4.7 Connectedness.- 2.5 Quantum and Classical Relativities.- 2.6 Sums Over Paths.- 2.7 Discrete Quantum Theory.- 2.8 Summary.- 3. Classical Matrix Mechanics.- 3.1 Operations and Cooperations.- 3.1.1 Classical Operators.- 3.1.2 Classical Cooperations and Coarrows.- 3.1.3 Linearization.- 3.1.4 Vacuum.- 3.2 Ordinates and Coordinates.- 3.2.1 Classical Eigenvalue Principle.- 3.2.2 Spectral Analysis.- 3.2.3 Complete Coordinates.- 3.2.4 OR, XOR, and POR.- 3.2.5 Averages.- 3.2.6 Framed Algebras.- 3.3 Some Classical Systems.- 3.3.1 Bit.- 3.3.2 N-ring.- 3.3.3 Bin and Commuting Calculus.- 3.3.4 Bits and Anticommuting Calculus.- 3.3.5 Top Bin.- 3.3.6 Extended Bin.- 3.4 Summary.- 3.5 References.- 4. Quantum Jumps.- 4.1 Quantum Arrows and Coarrows.- 4.1.1 Quantum Operations.- 4.1.2 Quantum Systems Are Not Categories.- 4.2 Adjoints and Metrics.- 4.2.1 Quantum Types.- 4.2.2 Negative Norms.- 4.2.3 Projections.- 4.2.4 Quantum Coordinates.- 4.2.5 Interpretations of Coordinates.- 4.2.6 Projective Coordinates.- 4.2.7 Non-numerical Coordinates.- 4.3 Transformation Theory.- 4.3.1 Frames.- 4.3.2 Operator Kinematics, Quantum and Classical.- 4.3.3 Quantum Entity.- 4.4 Quantizing.- 4.4.1 Re-relativizing.- 4.4.2 Rephasing.- 4.4.3 Quantization and Non-Commutativity.- 4.5 Born-Malus Law.- 4.6 Quantum Logic.- 4.6.1 Quantum Binary Variables.- 4.6.2 Quantum OR, POR, and XOR.- 4.6.3 Quantum Cooperations.- 4.7 Indefinite Quantum Kinematics.- 4.8 Simple Quantum Systems.- 4.8.1 Bit.- 4.8.2 Bin.- 4.8.3 Projective Quantum Bin.- 4.8.4 Indeterminacy Principle.- 4.8.5 Hydrogen Atom.- 4.8.6 Photon and Ghost.- 4.9 Summary.- 5. Non-Objective Physics.- 5.1 Descartes’ Mathesis.- 5.2 Newton’s Aether.- 5.2.1 Partial Reflection and Interference.- 5.2.2 Polarization.- 5.2.3 Diffraction.- 5.2.4 Quantum Principle.- 5.3 Planck’s Constants.- 5.3.1 k is for Thermodynamics.- 5.3.2 c is for Special Relativity.- 5.3.3 G is for Gravity.- 5.3.4 h is for Quantum Theory.- 5.3.5 Planck Units.- 5.4 Einstein’s Quantum.- 5.4.1 Photoelectric Effect.- 5.4.2 Unified Fields.- 5.4.3 How Did Newton Know?.- 5.5 Bohr’s Atom.- 5.5.1 Correspondence Principle.- 5.6 Post-quantum Theories.- 5.6.1 Theory S.- 5.6.2 Theory N.- 5.6.3 Theory O.- 5.6.4 Theory E.- 5.6.5 Why So Many Theories?.- 6. Why Vectors?.- 6.1 Fundamental Theorem (Weak Form).- 6.2 Galois Lattices and Galois Connection.- 6.3 Multiplicity.- 6.4 Logic-based Arithmetic.- 6.4.1 Quantum-Logical Addition.- 6.4.2 Quantum-Logical Multiplication.- 6.5 Fundamental Theorem (Strong Form).- 6.5.1 Occlusion.- 6.5.2 Identification.- 6.5.3 Adjoint.- 6.5.4 Modularity.- 6.5.5 Irreducibility.- 6.5.6 Desarguesian Postulate.- 6.5.7 Proofs.- 6.6 Generators.- 6.7 Critique of the Lattice Logic.- 6.8 Summary.- Act 2 Many.- 7. Many Quanta.- 7.1 Classical Combinatorics.- 7.1.1 Ordered Pairs of Units.- 7.1.2 Unordered Pairs of Units.- 7.1.3 Symmetry and Duality.- 7.1.4 Sequence.- 7.1.5 Series.- 7.1.6 Sib.- 7.1.7 Set.- 7.2 Quantum Combinatorics.- 7.2.1 Quantum Sequence.- 7.2.2 Quantum Series.- 7.2.3 Quantum Sib.- 7.2.4 Quantum Set.- 7.3 Singleton.- 7.4 Why Tensors?.- 7.5 Summary.- 8. Quantum Probability and Improbability.- 8.1 Quantum Law of Large Numbers.- 8.1.1 Weak Law of Large Numbers.- 8.1.2 Strong Law of Large Numbers.- 8.2 Mixed Operations.- 8.2.1 Superpositions and Mixtures.- 8.2.2 Diffuse Initial Actions.- 8.2.3 Diffuse Final Actions.- 8.2.4 Diffuse Medial Actions.- 8.2.5 Coherent Cooperators.- 8.3 Classical Limit.- 8.3.1 Coherent States.- 8.3.2 Macroscopic Measurement.- 8.3.3 Equatorial Bulge.- 8.3.4 Coherent Plane.- 8.3.5 The ?qcs Process.- 8.4 Hidden States.- 9. The Search for Pangloss.- 9.1 Aristotle.- 9.2 Llull and Bruno.- 9.3 Leibniz.- 9.4 Grassmann.- 9.4.1 Extensors.- 9.4.2 Extensor Terminology.- 9.5 Boole.- 9.6 Peirce.- 9.6.1 Tychistic Logical Algebra.- 9.6.2 Synechism and Quantum Condensation.- 9.6.3 Nomic Evolution.- 9.7 Peano.- 9.8 Clifford.- 9.9 Summary.- 10. Quantum Set Algebra.- 10.1 Remarks on Set Algebra.- 10.2 Tensor Algebra of Sets.- 10.2.1 Opposite.- 10.2.2 Degree.- 10.2.3 Extensor Structure.- 10.2.4 Bases.- 10.2.5 Products.- 10.2.6 Complement.- 10.3 Recursive Construction.- 10.4 Infinite Sets.- 10.5 Classical, Mixed and Fully Quantum Set Algebras.- 10.6 Clifford Algebra.- 10.6.1 Classes as Clifford Extensors.- 10.6.2 Real Quantum Theory.- 10.6.3 Episystemic Variables.- 10.6.4 The Real World.- 10.7 Quantum Extensors.- 10.8 Summary.- Act 3 One.- 11. Classical Spacetime.- 11.1 Flat Spacetime.- 11.1.1 Chronometry.- 11.1.2 Causal Symmetry Implies Minkowski.- 11.1.3 Spinors and Minkowski.- 11.2 Causal Symmetries.- 11.2.1 Null Symmetric Metric.- 11.2.2 Poincaré.- 11.2.3 Lorentz.- 11.2.4 Infinitesimal Lorentz.- 11.3 Einstein Locality.- 11.3.1 Equivalence Principle.- 11.3.2 General Relativization.- 11.4 The Idea of Gauge.- 11.5 Tensor Differential Calculus.- 11.5.1 Covariant Derivative.- 11.5.2 Distortion.- 11.5.3 Curvature.- 11.5.4 Ricci Tensor.- 11.5.5 Torsion Tensor.- 11.6 Gravity.- 11.6.1 Special Relativistic Gravity.- 11.6.2 Einstein Gravity.- 11.7 Spin.- 11.7.1 Spinors and Polyspinors.- 11.7.2 Spin Algebra.- 11.7.3 Sesquispinors.- 11.7.4 Spin Adjoint.- 11.7.5 Spacetime Decomposition of Spin.- 11.7.6 Dirac Spinors.- 11.8 Spin Gauge.- 11.9 Summary.- 12. Semi-quantum Dynamics.- 12.1 Propagator.- 12.1.1 Forward Propagation.- 12.1.2 Classical Propagation.- 12.1.3 Quantum Propagation.- 12.1.4 Backward Propagation.- 12.1.5 The Measurement Problem.- 12.1.6 Generators.- 12.2 Classical Dynamics.- 12.2.1 Phase Space.- 12.2.2 Least Time Principle.- 12.2.3 Endpoint Variations.- 12.2.4 Variational Derivative.- 12.2.5 Stationary Phase.- 12.2.6 Action Principle.- 12.2.7 Hamiltonian Dynamics.- 12.3 Canonical Quantization.- 12.3.1 Quantum Energy.- 12.3.2 Coherent states.- 12.4 Quantum Dynamics.- 12.4.1 Real Time and Sample Time.- 12.4.2 Quantum Connection.- 12.4.3 Heisenberg Picture.- 12.4.4 Schrödinger Picture.- 12.4.5 Time-dependent Dynamics.- 12.5 Quantum Action Principle.- 12.5.1 Path Amplitude.- 12.5.2 Path Tensor.- 12.5.3 Hamiltonian and Lagrangian Theories.- 12.5.4 Schwinger Variational Principle.- 12.5.5 Superquantum Theory.- 12.5.6 What do Physicists Want?.- 12.6 Summary.- 13. Local Dynamics.- 13.1 Local Fields.- 13.2 Gauge Physics.- 13.2.1 Gauge History.- 13.2.2 Standard Model.- 13.2.3 Measuring the Gauge Connection.- 13.3 Odd Fields.- 13.4 Energy.- 13.5 Quantum Locality.- 14. Quantum Set Calculus.- 14.1 Why Set Calculus?.- 14.1.1 Interpretations of Set Theory.- 14.1.2 Activated Set Theory.- 14.1.3 Classical Pure Sets.- 14.2 Random Sets.- 14.2.1 First-Order Random Sets.- 14.2.2 Grassmann Algebra of the Random Set.- 14.3 The Quantum Set.- 14.3.1 Higher-Order Quantum Set.- 14.3.2 Operators of the Quantum Set.- 14.3.3 Does Unitizing Respect Degree?.- 14.3.4 Tensor Set Theory.- 14.3.5 Order.- 14.3.6 Metastatistics.- 14.3.7 Quantum Lambda Calculus.- 14.4 Act Algebra.- 14.5 Quantum Mapping.- 14.6 Summary.- 15. Quantum Groups and Operons.- 15.1 Motivations.- 15.2 Double Operations.- 15.2.1 Algebraic Preliminaries.- 15.2.2 Classical Double Arrows.- 15.2.3 Classical Double Semigroup and Algebra.- 15.3 The Operon Concept.- 15.4 Quantum Operon.- 15.5 Quantum Double Arrows.- 15.5.1 Unit and Inversor.- 15.6 Examples.- 15.6.1 Quantum Plane.- 15.6.2 Quantum Four-group.- 15.6.3 Operation Semigroup.- 15.6.4 Operon Diagrams.- 15.6.5 Pair Monoids.- 15.6.6 Projective Quantum Groups.- 15.7 Coherent Group of a Quantum Monoid.- 15.8 Summary.- Act 4 Nothing.- 16. Quantum Spacetime Net.- 16.1 Quantum Topology.- 16.2 Quantum Spacetime Past.- 16.2.1 Hyperspace.- 16.2.2 Infraspace.- 16.2.3 Microstructure.- 16.3 Quantum Spacetime Present.- 16.3.1 Causal Spacetime Network.- 16.3.2 Causal Relation and Successor Relation.- 16.3.3 Hyperalgebra.- 16.3.4 Simplicial Complex Theory.- 16.3.5 Membership Theory.- 16.3.6 Vertex Theory.- 16.3.7 Graph Theory.- 16.3.8 Inclusion Theory.- 16.3.9 Choosing a Spacetime Theory.- 16.4 Quantum Spacetime Nets.- 16.4.1 Correspondence.- 16.4.2 Net Diagrams.- 16.4.3 Quantizing Discrete Spacetimes.- 16.4.4 Net Notation.- 16.4.5 The Supercrystalline Vacuum.- 16.5 Spin.- 16.5.1 Discrete Spin.- 16.5.2 Quantum Spin.- 16.5.3 Indefinite Spin Metric.- 16.5.4 Coherent Spin.- 16.6 Flat Spacetime.- 16.6.1 Discrete Poincaré Group.- 16.6.2 Minkowski Spacetime.- 16.6.3 Quantum Poincaré Group.- 16.6.4 Coherent Translation Group.- 16.7 Internal Groups.- 16.7.1 QND Gauge Symmetries.- 16.7.2 Commutation Relations of the Standard Model.- 16.8 Quantum Network Dynamics.- 16.8.1 Network Charges and Fluxes.- 16.8.2 The Unitary Groups.- 16.8.3 QND Action Principle.- 16.9 Summary.- 17. Toolshed.- 17.1 Recursive Constructions.- 17.1.1 Logic and Sets.- 17.1.2 Acts.- 17.2 Algebra.- 17.2.1 Semigroup and Group.- 17.2.2 Category.- 17.2.2.1 Graph.- 17.2.2.2 Complex.- 17.2.2.3 Diagram.- 17.2.3 Group.- 17.2.4 Ring, Algebra, Module, Vector Space.- 17.2.5 Group Representation.- 17.2.6 Involutions.- 17.2.7 Lie Algebra.- 17.2.8 Tensor.- 17.2.9 Manifold.- 17.2.9.1 Tensor Calculus.- 17.2.9.2 Gauge.- 17.3 Order Concepts.- 17.3.1 Projective Geometry.- 17.3.2 Order Structures.- 17.3.3 Relation.- 17.4 Topology.- 17.5 Perturbation Methods.- 17.5.1 Discrete Perturbation Theory.- 17.5.2 Double Operators.- 17.5.3 Perturbation Series.- 17.5.4 Continuous Perturbation Theory.- 17.6 Hilbert Space and † Space.- 17.7 Notation.- 17.7.1 Indices.- 17.7.2 Mathematical Symbols and Abbreviations.

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